Constructions of cocycles over irrational rotations

W. Bułatek; M. Lemańczyk; D. Rudolph

Studia Mathematica (1997)

  • Volume: 125, Issue: 1, page 1-11
  • ISSN: 0039-3223

Abstract

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We construct a coboundary cocycle which is of bounded variation, is homotopic to the identity and is Hölder continuous with an arbitrary Hölder exponent smaller than 1.

How to cite

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Bułatek, W., Lemańczyk, M., and Rudolph, D.. "Constructions of cocycles over irrational rotations." Studia Mathematica 125.1 (1997): 1-11. <http://eudml.org/doc/216418>.

@article{Bułatek1997,
abstract = {We construct a coboundary cocycle which is of bounded variation, is homotopic to the identity and is Hölder continuous with an arbitrary Hölder exponent smaller than 1.},
author = {Bułatek, W., Lemańczyk, M., Rudolph, D.},
journal = {Studia Mathematica},
keywords = {ergodic transformations; skew products; irrational rotations; cocycles},
language = {eng},
number = {1},
pages = {1-11},
title = {Constructions of cocycles over irrational rotations},
url = {http://eudml.org/doc/216418},
volume = {125},
year = {1997},
}

TY - JOUR
AU - Bułatek, W.
AU - Lemańczyk, M.
AU - Rudolph, D.
TI - Constructions of cocycles over irrational rotations
JO - Studia Mathematica
PY - 1997
VL - 125
IS - 1
SP - 1
EP - 11
AB - We construct a coboundary cocycle which is of bounded variation, is homotopic to the identity and is Hölder continuous with an arbitrary Hölder exponent smaller than 1.
LA - eng
KW - ergodic transformations; skew products; irrational rotations; cocycles
UR - http://eudml.org/doc/216418
ER -

References

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  1. [1] H. Anzai, Ergodic skew product transformations on the torus, Osaka J. Math. 3 (1951), 83-99. Zbl0043.11203
  2. [2] H. Furstenberg, Strict ergodicity and transformations on the torus, Amer. J. Math. 83 (1961), 573-601. Zbl0178.38404
  3. [3] P. Gabriel, M. Lemańczyk et P. Liardet, Ensemble d'invariants pour les produits croisés de Anzai, Mem. Soc. Math. France 119 (1991). Zbl0754.28011
  4. [4] M. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. IHES 49 (1979), 5-234. 
  5. [5] A. Iwanik, M. Lemańczyk and D. Rudolph, Absolutely continuous cocycles over irrational rotations, Israel J. Math. 83 (1993), 73-95. Zbl0786.28011
  6. [6] A. B. Katok, Constructions in Ergodic Theory, unpublished lecture notes. 
  7. [7] A. V. Kochergin, On the homology of functions over dynamical systems, Dokl. Akad. Nauk SSSR 231 (1976), 795-798. Zbl0414.28024
  8. [8] M. Lemańczyk and Ch. Mauduit, Ergodicity of a class of cocycles over irrational rotations, J. London Math. Soc. 49 (1994), 124-132. Zbl0801.28009
  9. [9] D. Rudolph, ℤ n and ℕ n cocycle extensions and complementary algebras, Ergodic Theory Dynam. Systems 6 (1986), 583-599. 
  10. [10] A. Zygmund, Trigonometric Series, Vol. I, Cambridge Univ. Press, 1959. Zbl0085.05601

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